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Science: The flight of a beer bubble from first principles

9 November 1991

By ANDY COGHLAN

Next time life is getting too much for you and you find yourself staring
despondently into a glass of beer, consider the wonders of physics taking
place before your very eyes. Did you know, for example, that the bubbles
of carbon dioxide which give beer its fizz remain spherical until their
radius exceeds a third of a millimetre, when they become ellipsoidal? Or
that new bubbles enter the bulk of the beer every half second?

Neil Shafer and Richard Zare of Stanford University in California describe
the physics of beer bubbles in the October issue of Physics Today. ‘No one
has quantitatively described the flight of a beer bubble from first principles,’
they write. ‘Once you begin to learn about the nature of beer bubbles, you
will never again look at a glass of beer in quite the same way.’

They point out that beer bubbles form in much the same way that rain
clouds form in the atmosphere. But while rain droplets form around airborne
particles of dust, bubbles of carbon dioxide nucleate mainly in the microscopic
crannies on the inner surface of the beer glass.

They point out that individual bubbles begin life as invisible clusters
– or microbubbles – of carbon dioxide. These grow on the nucleation sites
by absorbing additional molecules of carbon dioxide from the bulk of the
beer. Once they reach a critical size, they cleave off into the liquid.

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The bubbles continue growing as they ascend by subsuming more carbon
dioxide. ‘In other words, bubbles act as nucleation centres for themselves,’
say Shafer and Zare. One reason for this is that when people open a beer,
the partial pressure of the dissolved carbon dioxide exceeds the pressure
of carbon dioxide in the bubble, so the dissolved gas migrates rapidly to
the bubble.

Shafer and Zare point out that as soon as one bubble is released, another
starts to form, and because each bubble forms in the same way, the bubbles
cleave off at a constant rate. For example, they observed that 107 bubbles
reached the top of a beer glass in 58 seconds, so that one left the nucleation
site every 0.54 seconds. The radius of the bubbles grew at 4 hundredths
of a millimetre a second.

Shafer and Zare also found that bubbles accelerate as they approach
the top of the glass. ‘The upward buoyancy force increases more quickly
than the downward drag force, causing the bubble to accelerate,’ they say.
This accounts for the fact that bubbles in a stream from the bottom are
more widely spaced towards the top of the glass.

The researchers say that surfactants added to the beer cause the foamy
head to form on the surface, but also affect the trajectory of bubbles because
they form a rigid wall around them. This effectively makes the bubble ascend
more slowly than would be predicted from their model.

They say that under the influence of the surfactants, the bubbles are
more likely to form ellipsoid shapes, but conventional beer glasses are
too shallow and the bubbles too small for drinkers to be able to observe
these effects. However, Shafer and Zare add that if bubbles have the opportunity
to grow to a radius of around 1 millimetre – as they could in a ‘yard’ of
ale, for example – the radius would oscillate, making the bubble change
from a straight to a zigzag or helical path.

‘The deformation, oscillation, wandering and ultimate breakup of a rising,
rapidly growing bubble make beer bubble dynamics a rich phenomenon, worthy
of study in the laboratory as well as the pub,’ say Shafer and Zare.